Finite Group Databasebeta

C23×C4×D172 #26003163

order11008
isoclinismisoclinic class of Dic86
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C215

Aliases

direct productC23×C4×D172

Splittings

FittingC23×C42×C43 ⋊ C2
SylowC43 ⋊ C23×C4×D4

Subgroups

subgroupG/H
centerC24×C4C2×D43
commutatorC2×C43C25×C4
FrattiniC22C25×D43
FittingC23×C42×C43C2
socleC25×C43C23
prime radicalC24×D172C2
cosocleC22×C43C26
hypercenterC23×C42D43
hypocenterC43C23×C4×D4
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C24×C4 ◁ C23×C42

19998 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2848 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1076134);