Finite Group Databasebeta

C22×C4⋊C8×D53 #28247698

order13568
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C210

Aliases

direct productC22×C4⋊C8×D53

Splittings

FittingC22×C4⋊C8×C53 ⋊ C2
SylowC53 ⋊ C23×C4⋊C8

Subgroups

subgroupG/H
centerC23×C4C22×D53
commutatorC2×C53C24×C8
FrattiniC2×C4C24×D53
FittingC22×C4⋊C8×C53C2
socleC24×C53C22×C4
prime radicalC24×D53C2×C4
cosocleC2×C4×C53C25
hypercenterC22×C4⋊C8D53
hypocenterC53C23×C4⋊C8
LCSG ▷ C2×C53 ▷ C53
UCSC1 ◁ C23×C4 ◁ C22×C4⋊C8

3870 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6784

Conjugacy classes & character table

2240 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 1033174);