Finite Group Databasebeta

C2×#19132834 #25018253

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C210

Aliases

direct productC2×#19132834

Splittings

FittingC23×C22⋊C4×C43 ⋊ C2
SylowC43 ⋊ C2×#1438

Subgroups

subgroupG/H
centerC25C22×D43
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC23×C22⋊C4×C43C2
socleC25×C43C23
prime radicalC24×C22⋊D43C2
cosocleC24×C43C24
hypercenterC23×C22⋊C4D43
hypocenterC43C2×#1438
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C25 ◁ C23×C22⋊C4

8190 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1768 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 91224);