Finite Group Databasebeta

#107×D172 #25114716

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct product#107×D172

Splittings

FittingC4×#107×C43 ⋊ C2
SylowC43 ⋊ D4×#107

Subgroups

subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC4×#107×C43C2
socleC23×C43C22×D4
prime radicalC22×D172D4
cosocleC22×C4×C43C24
hypercenterC4×#107D43
hypocenterC43D4×#107
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#107

1126 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, 187687);