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C2×C5×C13×D31 #22549013

order8060
isoclinismisoclinic class of D31
automorphism?
homologyAbelianization (H1) = C22×C5×C13 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C13×D31

Splittings

Fitting, socleC2×C5×C13×C31 ⋊ C2
derived, SylowC31 ⋊ C22×C5×C13
HallC5×C13×C31 ⋊ C22
HallC13×C31 ⋊ C22×C5
HallC5×C31 ⋊ C22×C13

Subgroups

subgroupG/H
center, hypercenterC2×C5×C13D31
commutator, hypocenterC31C22×C5×C13
FrattiniC1G
Fitting, socleC2×C5×C13×C31C2
LCSG ▷ C31
UCSC1 ◁ C2×C5×C13

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2210 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C5×C13×D31⋊C3, C2×C5×#14559023, C2×C5×#14559022, …
maximal normal subgroup ofC2×C5×C13×D31⋊C3, C2×C5×#14559023, C2×C5×#14559022, …
maximal quotient ofC5×D3×C13×D31, C2×C3×C5×C13×D31, C2×C5×C13×D93

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8060, 46);