Finite Group Databasebeta

C22×(C2×D367)⋊C4 #37554633

order23488
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC22×(C2×D367)⋊C4

Splittings

FittingC23×C4×C367 ⋊ C2
SylowC367 ⋊ C22×C22⋊C4

Subgroups

subgroupG/H
centerC24C2×D367
commutatorC2×C367C23×C4
FrattiniC22C23×D367
FittingC23×C4×C367C2
socleC24×C367C22
prime radicalC24×D367C2
cosocleC22×C367C24
hypercenterC23×C4D367
hypocenterC367C22×C22⋊C4
LCSG ▷ C2×C367 ▷ C367
UCSC1 ◁ C24 ◁ C23×C4

674 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, 996);