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C2×C5×D7×C67 #22627751

order9380
isoclinismisoclinic class of D7
automorphism?
homologyAbelianization (H1) = C22×C5×C67 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×D7×C67
unambiguous semidirect productC7⋊(C22×C5×C67)
unambiguous semidirect product(C2×C7)⋊(C2×C5×C67)

Splittings

Fitting, socleC2×C5×C7×C67 ⋊ C2
derived, SylowC7 ⋊ C22×C5×C67
HallC5×C7×C67 ⋊ C22
HallC7×C67 ⋊ C22×C5
HallC5×C7 ⋊ C22×C67

Subgroups

subgroupG/H
center, hypercenterC2×C5×C67D7
commutator, hypocenterC7C22×C5×C67
FrattiniC1G
Fitting, socleC2×C5×C7×C67C2
LCSG ▷ C7
UCSC1 ◁ C2×C5×C67

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3350 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C5×AGL(1,𝔽7)×C67, C2×C5×#14584200, C2×C5×#14584199, …
maximal normal subgroup ofC2×C5×AGL(1,𝔽7)×C67, C2×C5×#14584200, C2×C5×#14584199, …
maximal quotient ofC5×D3×D7×C67, C2×C3×C5×D7×C67, C2×C5×D21×C67

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9380, 26);