Finite Group Databasebeta

C2×#21447972 #29834643

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

Aliases

direct productC2×#21447972

Splittings

SylowC61 ⋊ C2×#2227

Subgroups

subgroupG/H
centerC23C2×D488
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC2×C61×C4⋊C16C2
socle, prime radicalC23×C61C2×D8
hypercenterC2×C4⋊C16D61
hypocenterC61C2×#2227
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×C4⋊C16

574 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15616

Conjugacy classes & character table

2458 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 324198);