Finite Group Databasebeta

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C2×C5×C7×D67 #22627752

order9380
isoclinismisoclinic class of D67
automorphism?
homologyAbelianization (H1) = C22×C5×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C7×D67
unambiguous semidirect productC67⋊(C22×C5×C7)
unambiguous semidirect product(C2×C67)⋊(C2×C5×C7)

Splittings

Fitting, socleC2×C5×C7×C67 ⋊ C2
derived, SylowC67 ⋊ C22×C5×C7
HallC5×C7×C67 ⋊ C22
HallC7×C67 ⋊ C22×C5
HallC5×C67 ⋊ C22×C7

Subgroups

subgroupG/H
center, hypercenterC2×C5×C7D67
commutator, hypocenterC67C22×C5×C7
FrattiniC1G
Fitting, socleC2×C5×C7×C67C2
LCSG ▷ C67
UCSC1 ◁ C2×C5×C7

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2450 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C5×C7×D67⋊C3, C2×C5×#14584196, C2×C5×#14584195, …
maximal normal subgroup ofC2×C5×C7×D67⋊C3, C2×C5×#14584196, C2×C5×#14584195, …
maximal quotient ofC5×D3×C7×D67, C2×C3×C5×C7×D67, C2×C5×C7×D201

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9380, 27);