Finite Group Databasebeta

C4×#14583696 #25960678

order11008
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC4×#14583696

Splittings

FittingC4×#135×C43 ⋊ C2
SylowC43 ⋊ C4×#575

Subgroups

subgroupG/H
centerC42D4×D43
commutatorC4×C43C24×C4
FrattiniC2×C4C24×D43
FittingC4×#135×C43C2
socleC22×C43C23×D4
prime radicalC2×#14583696C2
cosocleC2×C4×C43C25
hypercenterC4×#135D43
hypocenterC43C4×#575
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C42 ◁ C2×C42 ◁ C4×#135

2842 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1264 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1033649);