Finite Group Databasebeta

C2×#21421978 #28478737

order15104
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#21421978

Splittings

SylowC59 ⋊ C2×#1295

Subgroups

subgroupG/H
centerC24(C2×D59)⋊C4
commutatorC2×C4×C59C2×C42
FrattiniC2×C42C22×D59
FittingC22×#97×C59C2
socle, prime radicalC24×C59C22⋊C4
cosocleC2×C42×C59C23
hypercenterC22×#97D59
hypocenterC59C2×#1295
LCSG ▷ C2×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C24 ◁ C22×C42 ◁ C22×#97

830 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15104

Conjugacy classes & character table

2396 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 59616);