Finite Group Databasebeta

C2×#21443727 #29570374

order15616
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#21443727

Splittings

SylowC61 ⋊ C2×#1306

Subgroups

subgroupG/H
centerC23#14519684
commutatorC23×C61C2×C42
FrattiniC23×C4C22×D61
FittingC2×C61×#381C2
socleC23×C61#95
prime radicalC25×C61C2×C4
cosocleC23×C4×C61C23
hypercenterC2×#381D61
hypocenterC61C2×#1306
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#381

942 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

1732 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 59929);