Finite Group Databasebeta

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C2×C3×C5⋊(C7⋊D77) #44568942

order32340
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C7

Aliases

direct productC2×C3×C5⋊(C7⋊D77)
unambiguous semidirect product(C2×C5)⋊(C3×C7⋊D77)
unambiguous semidirect product(C2×C11)⋊(C3×C5⋊(C7⋊D7))

Splittings

Fitting, socleC2×C3×C5×C72×C11 ⋊ C2
derived, HallC5×C72×C11 ⋊ C22×C3
HallC3×C5×C72×C11 ⋊ C22
HallC3×C72×C11 ⋊ C2×D5
HallC3×C5×C72 ⋊ C2×D11
HallC72×C11 ⋊ C2×C3×D5
HallC5×C72 ⋊ C2×C3×D11
HallC3×C5×C11 ⋊ C2×C7⋊D7
HallC3×C72 ⋊ C2×D55
HallC5×C11 ⋊ C2×C3×C7⋊D7
SylowC72 ⋊ C2×C3×D55
HallC3×C11 ⋊ C2×C5⋊(C7⋊D7)
HallC3×C5 ⋊ C2×C7⋊D77
SylowC11 ⋊ C2×C3×C5⋊(C7⋊D7)
SylowC5 ⋊ C2×C3×C7⋊D77

Subgroups

subgroupG/H
center, hypercenterC2×C3C5⋊(C7⋊D77)
commutator, cosocle, hypocenterC5×C72×C11C22×C3
FrattiniC1G
Fitting, socleC2×C3×C5×C72×C11C2
LCSG ▷ C5×C72×C11
UCSC1 ◁ C2×C3

400 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16170

Conjugacy classes & character table

8094 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 644);