#13062004

order	1344
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center, Fitting, hypercenter	C₄	SO(3,𝔽₇)
commutator, cosocle, hypocenter	SL(2,𝔽₇)	C₂²
Frattini, socle	C₂	C₂×SO(3,𝔽₇)
LCS	G ▷ SL(2,𝔽₇)
UCS	C₁ ◁ C₄

83 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 2 generators on 32 points:

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

Conjugacy classes & character table

32 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₃×#13062004
maximal normal subgroup of	C₃×#13062004
maximal quotient of	C₄×#10621462, C₃×#13062004

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 11293);