Finite Group Databasebeta

#117×Dic86 #25256025

order11008
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C27×C4

Aliases

direct product#117×Dic86

Splittings

SylowC43 ⋊ Q8×#117

Subgroups

subgroupG/H
centerC22×C4C23×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC4×#117×C43C2
socle, cosocleC23×C43C25
prime radicalC24×C43C24
hypercenterC4×#117D43
hypocenterC43Q8×#117
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C4×#117

2434 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1780 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 328996);