Finite Group Databasebeta

C8×#14273701 #28594717

order15104
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC8×#14273701

Splittings

FittingC22×C4×C8×C59 ⋊ C2
SylowC59 ⋊ C8×#121

Subgroups

subgroupG/H
centerC22×C8C22×D59
commutatorC22×C59C23×C8
FrattiniC22×C4C23×D59
FittingC22×C4×C8×C59C2
socleC23×C59C23×C4
prime radicalC2×#14273701C4
cosocleC22×C4×C59C24
hypercenterC22×C4×C8D59
hypocenterC59C8×#121
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C22×C8 ◁ C22×C4×C8

1222 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

3824 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 175596);