Finite Group Databasebeta

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C4×C22⋊Dic193 #27135107

order12352
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4

Aliases

direct productC4×C22⋊Dic193

Splittings

SylowC193 ⋊ C4×C22⋊C4

Subgroups

subgroupG/H
centerC22×C4C2×D193
commutatorC2×C193C2×C42
FrattiniC23C22×D193
FittingC23×C4×C193C2
socle, cosocleC23×C193C23
prime radicalC24×C193C22
hypercenterC23×C4D193
hypocenterC193C4×C22⋊C4
LCSG ▷ C2×C193 ▷ C193
UCSC1 ◁ C22×C4 ◁ C23×C4

258 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, 397);