Finite Group Databasebeta

C22×#15690538 #27136018

order12352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC22×#15690538

Splittings

FittingC22×C8×C193 ⋊ C2
SylowC193 ⋊ C22×M16

Subgroups

subgroupG/H
centerC22×C4C2×D193
commutatorC2×C193C23×C4
FrattiniC4C23×D193
FittingC22×C8×C193C2
socleC23×C193C2×C4
prime radicalC23×D193C4
cosocleC4×C193C24
hypercenterC22×C8D193
hypocenterC193C22×M16
LCSG ▷ C2×C193 ▷ C193
UCSC1 ◁ C22×C4 ◁ C22×C8

298 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3112 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12352, 1308);