Finite Group Databasebeta

C2×#21443691 #29569925

order15616
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23

Aliases

direct productC2×#21443691

Splittings

SylowC61 ⋊ C2×#1291

Subgroups

subgroupG/H
centerC23#14519684
commutatorC2×C4×C61C2×C42
FrattiniC2×C42C22×D61
FittingC2×C4×M16×C61C2
socleC23×C61#95
prime radicalC24×C61C4⋊C4
cosocleC2×C42×C61C23
hypercenterC2×C4×M16D61
hypocenterC61C2×#1291
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×C4×M16

610 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7808

Conjugacy classes & character table

2464 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 59480);