Finite Group Databasebeta

C2×#21421931 #28478145

order15104
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×#21421931

Splittings

SylowC59 ⋊ C2×#1277

Subgroups

subgroupG/H
centerC23×C4D236
commutatorC4×C59C2×C4×C8
FrattiniC2×C42C22×D59
FittingC22×C4×C8×C59C2
socle, prime radicalC24×C59C4⋊C4
cosocleC2×C42×C59C23
hypercenterC22×C4×C8D59
hypocenterC59C2×#1277
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23×C4 ◁ C22×C42 ◁ C22×C4×C8

830 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15104

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, 59024);