Finite Group Databasebeta

C2×D4⋊C8×D61 #29646353

order15616
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C27

Aliases

direct productC2×D4⋊C8×D61

Splittings

FittingC2×C61×D4⋊C8 ⋊ C2
SylowC61 ⋊ C22×D4⋊C8

Subgroups

subgroupG/H
centerC22×C4D4×D61
commutatorC4×C61C23×C8
FrattiniC42C23×D61
FittingC2×C61×D4⋊C8C2
socleC23×C61C2×C22⋊C4
prime radicalC22×D4×D61C4
cosocleC42×C61C24
hypercenterC2×D4⋊C8D61
hypocenterC61C22×D4⋊C8
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×D4⋊C8

1886 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

1792 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 135908);