D₄×#3861 #11924260

order	1176
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	D₄×#3861
unambiguous semidirect product	C₄⋊(C₂×#3861)

Fitting, Hall	C₇²×D₄ ⋊ C₃
Sylow	C₇² ⋊ C₃×D₄

160 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 196

A minimal faithful permutation representation — 3 generators on 18 points:

(1,2,3,4)(6,7,8)(9,11,10)(13,14,15)(16,18,17);(2,4)(12,13,14,16,15,17,18);(5,6,7,9,8,10,11)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1176, 175);