Finite Group Databasebeta

C2×#21444706 #29649744

order15616
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

direct productC2×#21444706

Splittings

FittingC2×C61×Q8⋊C8 ⋊ C2
SylowC61 ⋊ C2×#1590

Subgroups

subgroupG/H
centerC22×C4D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC2×C61×Q8⋊C8C2
socleC23×C61C4×D4
prime radicalC22×D244C2×C4
cosocleC42×C61C24
hypercenterC2×Q8⋊C8D61
hypocenterC61C2×#1590
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×Q8⋊C8

746 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7808

Conjugacy classes & character table

1768 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 139299);