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C2×C3×C5×D91 #19129882

order5460
isoclinismisoclinic class of D91
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C5×D91

Splittings

Fitting, socleC2×C3×C5×C7×C13 ⋊ C2
derived, HallC7×C13 ⋊ C22×C3×C5
HallC3×C5×C7×C13 ⋊ C22
HallC5×C7×C13 ⋊ C22×C3
HallC3×C7×C13 ⋊ C22×C5
HallC3×C5×C13 ⋊ C2×D7
HallC3×C5×C7 ⋊ C2×D13
HallC5×C13 ⋊ C2×C3×D7
HallC3×C13 ⋊ C2×C5×D7
HallC5×C7 ⋊ C2×C3×D13
HallC3×C7 ⋊ C2×C5×D13
SylowC13 ⋊ C2×C3×C5×D7
SylowC7 ⋊ C2×C3×C5×D13

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5D91
commutator, hypocenterC7×C13C22×C3×C5
FrattiniC1G
Fitting, socleC2×C3×C5×C7×C13C2
LCSG ▷ C7×C13
UCSC1 ◁ C2×C3×C5

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1410 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C5×#13109902, C2×C5×#13109903, C2×C5×(C7⋊C9)⋊D13, …
maximal normal subgroup ofC2×C5×#13109902, C2×C5×#13109903, C2×C5×(C7⋊C9)⋊D13, …
maximal quotient ofC2×C5×C9×D91, C3×C5×D3×D91, C2×C3×C5×D273, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5460, 224);