Finite Group Databasebeta

C22×C8×D172 #25960430

order11008
isoclinismisoclinic class of Dic86
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C210

Aliases

direct productC22×C8×D172

Splittings

FittingC22×C4×C8×C43 ⋊ C2
SylowC43 ⋊ C22×C8×D4

Subgroups

subgroupG/H
centerC23×C8C2×D43
commutatorC2×C43C24×C8
FrattiniC2×C4C24×D43
FittingC22×C4×C8×C43C2
socleC24×C43C22×C4
prime radicalC23×D172C4
cosocleC2×C4×C43C25
hypercenterC22×C4×C8D43
hypocenterC43C22×C8×D4
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C23×C8 ◁ C22×C4×C8

3694 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, 1033401);