Finite Group Databasebeta

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C22×#15690534 #27135709

order12352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC22×#15690534

Splittings

SylowC193 ⋊ C22×C4⋊C4

Subgroups

subgroupG/H
centerC24C2×D193
commutatorC2×C193C23×C4
FrattiniC22C23×D193
FittingC23×C4×C193C2
socle, prime radicalC24×C193C22
cosocleC22×C193C24
hypercenterC23×C4D193
hypocenterC193C22×C4⋊C4
LCSG ▷ C2×C193 ▷ C193
UCSC1 ◁ C24 ◁ C23×C4

418 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, 999);