Finite Group Databasebeta

C2×#19145598 #25967853

order11008
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C27×C4

Aliases

direct productC2×#19145598

Splittings

SylowC43 ⋊ C2×#3215

Subgroups

subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC22×#124×C43C2
socleC23×C43C22×D4
prime radicalC23×D4×C43C22
hypercenterC22×#124D43
hypocenterC43C2×#3215
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C42 ◁ C22×#124

2242 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1228 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1040824);