Finite Group Databasebeta

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C2×C5×C67⋊C11 #20301426

order7370
automorphism?
homologyAbelianization (H1) = C2×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC2×C5×C67⋊C11
unambiguous semidirect product(C2×C67)⋊(C5×C11)
unambiguous semidirect product(C2×C5×C67)⋊C11

Splittings

Fitting, socle, HallC2×C5×C67 ⋊ C11
derived, SylowC67 ⋊ C2×C5×C11
HallC5×C67 ⋊ C2×C11
HallC2×C67 ⋊ C5×C11

Subgroups

subgroupG/H
center, hypercenterC2×C5C67⋊C11
commutator, hypocenterC67C2×C5×C11
FrattiniC1G
Fitting, socleC2×C5×C67C11
LCSG ▷ C67
UCSC1 ◁ C2×C5

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

170 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×C5×C67⋊C11, C5×Dic67⋊C11, Dic5×C67⋊C11, …
maximal normal subgroup ofC4×C5×C67⋊C11, C5×Dic67⋊C11, Dic5×C67⋊C11, …
maximal quotient ofC4×C5×C67⋊C11, C22×C5×C67⋊C11, C2×C3×C5×C67⋊C11, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7370, 2);