Finite Group Databasebeta

#108×D172 #25114851

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct product#108×D172

Splittings

FittingC4×#108×C43 ⋊ C2
SylowC43 ⋊ D4×#108

Subgroups

subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC4×#108×C43C2
socleC22×C43C22×C4⋊C4
prime radicalC22×D172Q8
cosocleC22×C4×C43C24
hypercenterC4×#108D43
hypocenterC43D4×#108
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#108

894 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1246 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 187822);