Finite Group Databasebeta

C2×#21422184 #28503557

order15104
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C24

Aliases

direct productC2×#21422184

Splittings

SylowC59 ⋊ C2×#1379

Subgroups

subgroupG/H
centerC22×C8D236
commutatorC4×C59C2×C4×C8
FrattiniC22×C8C22×D59
FittingC23×C16×C59C2
socleC23×C59C22⋊C8
prime radicalC24×C59M16
cosocleC22×C8×C59C23
hypercenterC23×C16D59
hypocenterC59C2×#1379
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C8 ◁ C23×C8 ◁ C23×C16

606 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

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, 84436);