Finite Group Databasebeta

C2×#21423000 #28558447

order15104
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

direct productC2×#21423000

Splittings

FittingC2×C59×#322 ⋊ C2
SylowC59 ⋊ C2×#1592

Subgroups

subgroupG/H
centerC22×C4C2×D236
commutatorC2×C4×C59C23×C4
FrattiniC42C23×D59
FittingC2×C59×#322C2
socleC23×C59C4×D4
prime radicalC22×D236C2×C4
cosocleC42×C59C24
hypercenterC2×#322D59
hypocenterC59C2×#1592
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C2×C4×C8 ◁ C2×#322

730 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

2384 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 139326);