Finite Group Databasebeta

C4×#16837633 #28595174

order15104
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×#16837633

Splittings

FittingC4×C22⋊Q8×C59 ⋊ C2
SylowC59 ⋊ C4×#465

Subgroups

subgroupG/H
centerC22×C4C2×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC4×C22⋊Q8×C59C2
socleC23×C59C22×D4
prime radicalC2×#14273701C22
cosocleC22×C4×C59C24
hypercenterC4×C22⋊Q8D59
hypocenterC59C4×#465
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×C22⋊Q8

1138 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

1712 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 176053);