Finite Group Databasebeta

C2×#21421929 #28478125

order15104
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4

Aliases

direct productC2×#21421929

Splittings

SylowC59 ⋊ C2×#1276

Subgroups

subgroupG/H
centerC2×C42D236
commutatorC4×C59C2×C4×C8
FrattiniC2×C42C22×D59
FittingC2×C43×C59C2
socleC23×C59#95
prime radicalC24×C59C22⋊C4
cosocleC2×C42×C59C23
hypercenterC2×C43D59
hypocenterC59C2×#1276
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C42 ◁ C22×C42 ◁ C2×C43

974 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

3824 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 59004);