Finite Group Databasebeta

C4×#16837224 #28504074

order15104
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4

Aliases

direct productC4×#16837224

Splittings

SylowC59 ⋊ C4×#365

Subgroups

subgroupG/H
centerC2×C4#14273658
commutatorC8×C59C2×C42
FrattiniC22×C8C22×D59
FittingC4×#106×C59C2
socleC22×C59C2×#106
prime radicalC23×C59C2×SD16
cosocleC22×C8×C59C23
hypercenterC4×#106D59
hypocenterC59C4×#365
LCSG ▷ C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ C4×#106

330 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

1688 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 84953);