Finite Group Databasebeta

C22⋊C4×D953 #44479376

order30496
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C24

Aliases

direct productC22⋊C4×D953

Splittings

FittingC22⋊C4×C953 ⋊ C2
SylowC953 ⋊ C2×C22⋊C4

Subgroups

subgroupG/H
center, FrattiniC22C22×D953
commutatorC2×C953C22×C4
FittingC22⋊C4×C953C2
socle, cosocleC22×C953C23
prime radicalC23×D953C2
hypercenterC22⋊C4D953
hypocenterC953C2×C22⋊C4
LCSG ▷ C2×C953 ▷ C953
UCSC1 ◁ C22 ◁ C22⋊C4

132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7624

Conjugacy classes & character table

4780 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30496, 96);