Finite Group Databasebeta

C8×#14273707 #28596105

order15104
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC8×#14273707

Splittings

FittingC8×C4⋊C4×C59 ⋊ C2
SylowC59 ⋊ C8×C22⋊Q8

Subgroups

subgroupG/H
centerC22×C8C22×D59
commutatorC22×C59C23×C8
FrattiniC22×C4C23×D59
FittingC8×C4⋊C4×C59C2
socleC23×C59C23×C4
prime radicalC23×D59C22×C4
cosocleC22×C4×C59C24
hypercenterC8×C4⋊C4D59
hypocenterC59C8×C22⋊Q8
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C22×C8 ◁ C8×C4⋊C4

990 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

2432 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 176984);