C₅×#16838446 #34062070

order	19110
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₅ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₅×#16838446

Splittings

Fitting, socle, Hall	C₅×C₇²×C₁₃ ⋊ C₂×C₃
derived, Hall	C₇²×C₁₃ ⋊ C₂×C₃×C₅
Hall	C₅×#14274263 ⋊ C₂
Hall	C₅×C₇⋊D₉₁ ⋊ C₃
Hall	#14274263 ⋊ C₂×C₅
Hall	C₇⋊D₉₁ ⋊ C₃×C₅
Hall	C₅×C₇² ⋊ D₁₃⋊C₃
Hall	C₅×C₁₃ ⋊ #64424
Sylow	C₇² ⋊ C₅×D₁₃⋊C₃
Sylow	C₁₃ ⋊ C₅×#64424

Subgroups

	subgroup	G/H
center, hypercenter	C₅	#16838446
commutator, cosocle, hypocenter	C₇²×C₁₃	C₂×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₇²×C₁₃	C₂×C₃
LCS	G ▷ C₇²×C₁₃
UCS	C₁ ◁ C₅

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 32
transitive degree	μ_t(G) = 3185

A minimal faithful permutation representation — 3 generators on 32 points:

(1,2,3,4,5)(7,11,12,8,9,13)(10,17,16,14,15,18)(20,23,24,21,22,25)(27,30,31,28,29,32);(6,7,10,9,13,16,15,17,18,12,11,14,8)(26,27,29,32,31,30,28);(19,20,22,25,24,23,21)

Conjugacy classes & character table

560 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅×#21439678, C₅×#21439599, C₅×#21439608, …
maximal normal subgroup of	C₅×#21439678, C₅×#21439599, C₅×#21439608, …
maximal quotient of	C₅×#21439522, C₂×C₅×#16838446

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19110, 63);

C5×#16838446 #34062070