Finite Group Databasebeta

C8×(C2×#6157)⋊C4 #28306355

order13568
automorphism?
homologyAbelianization (H1) = C42×C8 · Schur multiplier (H2) = C23×C42

Aliases

direct productC8×(C2×#6157)⋊C4

Splittings

FittingC2×C4×C8×C53 ⋊ C4
SylowC53 ⋊ C8×#95

Subgroups

subgroupG/H
centerC22×C8C2×#6157
commutatorC2×C53C42×C8
FrattiniC22×C4C22×#6157
FittingC2×C4×C8×C53C4
socleC23×C53C2×C42
prime radicalC23×D53C22×C4
cosocleC22×C4×D53C23
hypercenterC2×C4×C8#6157
hypocenterC53C8×#95
LCSG ▷ C2×C53 ▷ C53
UCSC1 ◁ C22×C8 ◁ C2×C4×C8

1174 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3392

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 1091831);