Finite Group Databasebeta

C4×#16838094 #28748597

order15104
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct productC4×#16838094

Splittings

FittingC4×C22⋊Q8×C59 ⋊ C2
SylowC59 ⋊ C4×#552

Subgroups

subgroupG/H
centerC22×C4C23×D59
commutatorC22×C59C24×C4
FrattiniC23C24×D59
FittingC4×C22⋊Q8×C59C2
socle, cosocleC23×C59C25
prime radicalC22×C22⋊D59C23
hypercenterC4×C22⋊Q8D59
hypocenterC59C4×#552
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C4×C22⋊Q8

2376 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

1724 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 329476);