D₂₃×D₂₅₃ #37551799

order	23276
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

direct product	D₂₃×D₂₅₃
unambiguous semidirect product	(C₁₁×D₂₃)⋊D₂₃
unambiguous semidirect product	(C₂₃×D₂₃)⋊D₁₁

Splittings

Fitting, socle, derived, Hall	C₁₁×C₂₃² ⋊ C₂²
Sylow	C₂₃² ⋊ C₂×D₁₁
Sylow	C₁₁ ⋊ D₂₃²

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₁×C₂₃²	C₂²
LCS	G ▷ C₁₁×C₂₃²
UCS	C₁

84 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 57
transitive degree	μ_t(G) = 506

A minimal faithful permutation representation — 2 generators on 57 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(12,13,15,17,19,21,23,25,27,29,31,33,34,32,30,28,26,24,22,20,18,16,14)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(54,55)(56,57);(1,2,4,6,8,10,11,9,7,5,3)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36,38,40,42,44,46,48,50,52,54,56,57,55,53,51,49,47,45,43,41,39,37)

Conjugacy classes & character table

1664 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23276, 89);

D23×D253 #37551799