Finite Group Databasebeta

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C22×D61⋊#100 #30625171

order15616
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC22×D61⋊#100
unambiguous semidirect productD61⋊(C22×#100)

Splittings

SylowC61 ⋊ C23×#100

Subgroups

subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C61C24×C4
FrattiniC22C24×#6923
FittingC23×D4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC23×D4×D61C2
cosocleC2×Dic61C25
hypercenterC23×D4#6923
hypocenterC61C23×#100
LCSG ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×D4

7134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1952

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1114726);