Finite Group Databasebeta

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C2×#21461932 #30616162

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

Aliases

direct productC2×#21461932
unambiguous semidirect productD61⋊#1949

Splittings

FittingC2×C4⋊C8×C61 ⋊ C4
SylowC61 ⋊ C2×#1949

Subgroups

subgroupG/H
centerC23C2×C4⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×C4⋊C8×C61C4
socleC23×C61C2×C4⋊C4
prime radicalC23×D61C2×D4
cosocleC2×C4×D61C24
hypercenterC2×C4⋊C8#6923
hypocenterC61C2×#1949
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4⋊C8

1142 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1105717);