#72219146

order	2400
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₁

non-solvable

Aliases

No aliases for this group.

Splittings

derived

C₅×SL(2,𝔽₅) ⋊ C₄

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₄	C₅⋊S₅
commutator, hypocenter	C₅×SL(2,𝔽₅)	C₄
Fitting	C₄×C₅	S₅
socle	C₂×C₅	A₅⋊C₄
prime radical, cosocle	C₅×#6732	C₂
LCS	G ▷ C₅×SL(2,𝔽₅)
UCS	C₁ ◁ C₄

99 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Permutation generators:

(1,16,8,18,6)(2,9,11,7,23)(12,17,27,33,32)(20,22,26,24,21);(2,27,8,26,25)(6,34,12,22,9)(7,19,21,18,17)(10,16,11,20,33);(2,17)(6,10)(7,25)(8,21)(9,16)(11,22)(12,20)(18,27)(19,26)(33,34);(4,14,30,29,36);(1,2,27,20)(4,14)(5,31)(6,7,33,26)(8,23,12,22)(9,32,21,18)(10,34)(11,17,24,16)(15,37)(19,25)(30,36)

Conjugacy classes & character table

60 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₃×#72219146, C₂×#72219146, D₅×GL(2,𝔽₅)
maximal normal subgroup of	C₃×#72219146, C₂×#72219146, D₅×GL(2,𝔽₅)
maximal quotient of	C₃×#72219146, C₂×#72219146

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from its permutation generators:

gap> G := Group((1,16,8,18,6)(2,9,11,7,23)(12,17,27,33,32)(20,22,26,24,21), (2,27,8,26,25)(6,34,12,22,9)(7,19,21,18,17)(10,16,11,20,33), (2,17)(6,10)(7,25)(8,21)(9,16)(11,22)(12,20)(18,27)(19,26)(33,34), (4,14,30,29,36), (1,2,27,20)(4,14)(5,31)(6,7,33,26)(8,23,12,22)(9,32,21,18)(10,34)(11,17,24,16)(15,37)(19,25)(30,36));