C₂¹¹×D₄ #72301774

order	16384
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂¹³ · Schur multiplier (H₂) = C₂⁷⁸

Aliases

direct product

C₂¹¹×D₄

Subgroups

	subgroup	G/H
center, socle	C₂¹²	C₂²
commutator, Frattini, cosocle	C₂	C₂¹³
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂¹² ◁ G
LECS	G ▷ C₂ ▷ C₁

74629802916129 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 8192

A minimal faithful permutation representation — 13 generators on 26 points:

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

Conjugacy classes & character table

10240 conjugacy classes. The character table is too large to display.

Relationships

automorphism group of

#10907, #10908, #11066, …

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((1,2)(24,26), (19,20)(21,22)(23,24)(25,26), (19,21)(20,22), (15,16)(17,18), (15,17)(16,18), (11,12)(13,14), (24,26), (23,24)(25,26), (11,13)(12,14), (7,8)(9,10), (7,9)(8,10), (3,4)(5,6), (3,5)(4,6));

C211×D4 #72301774