Finite Group Databasebeta

C24×Dic172 #26010379

order11008
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C214

Aliases

direct productC24×Dic172

Splittings

SylowC43 ⋊ C24×Q16

Subgroups

subgroupG/H
centerC25D172
commutator, cosocleC4×C43C26
FrattiniC4C25×D43
FittingC24×C8×C43C2
socle, prime radicalC25×C43D4
hypercenterC24×C8D43
hypocenterC43C24×Q16
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C25 ◁ C24×C4 ◁ C24×C8

11166 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2800 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1083350);