Finite Group Databasebeta

C2×#21422222 #28503667

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

Aliases

direct productC2×#21422222

Splittings

SylowC59 ⋊ C2×#1394

Subgroups

subgroupG/H
centerC23#14273641
commutatorC2×C4×C59C2×C42
FrattiniC22×Q8C22×D59
FittingC22×#101×C59C2
socleC23×C59#99
prime radicalC24×C59C22⋊C4
cosocleC22×Q8×C59C23
hypercenterC22×#101D59
hypocenterC59C2×#1394
LCSG ▷ C2×C4×C59 ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C24 ◁ C23×Q8 ◁ C22×#101

818 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

1328 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 84546);