Finite Group Databasebeta

C4×C22⋊Dic367 #37554034

order23488
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4

Aliases

direct productC4×C22⋊Dic367

Splittings

SylowC367 ⋊ C4×C22⋊C4

Subgroups

subgroupG/H
centerC22×C4C2×D367
commutatorC2×C367C2×C42
FrattiniC23C22×D367
FittingC23×C4×C367C2
socle, cosocleC23×C367C23
prime radicalC24×C367C22
hypercenterC23×C4D367
hypocenterC367C4×C22⋊C4
LCSG ▷ C2×C367 ▷ C367
UCSC1 ◁ C22×C4 ◁ C23×C4

258 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11744

Conjugacy classes & character table

5896 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23488, 397);