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C2×C13×D155 #22549009

order8060
isoclinismisoclinic class of D155
automorphism?
homologyAbelianization (H1) = C22×C13 · Schur multiplier (H2) = C2

Aliases

direct productC2×C13×D155
unambiguous semidirect product(C2×C5)⋊(C13×D31)
unambiguous semidirect product(C2×C31)⋊(D5×C13)

Splittings

Fitting, socleC2×C5×C13×C31 ⋊ C2
derived, HallC5×C31 ⋊ C22×C13
HallC5×C13×C31 ⋊ C22
HallC13×C31 ⋊ C2×D5
HallC5×C13 ⋊ C2×D31
SylowC31 ⋊ C2×D5×C13
SylowC5 ⋊ C2×C13×D31

Subgroups

subgroupG/H
center, hypercenterC2×C13D155
commutator, hypocenterC5×C31C22×C13
FrattiniC1G
Fitting, socleC2×C5×C13×C31C2
LCSG ▷ C5×C31
UCSC1 ◁ C2×C13

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2054 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C13×C5⋊(D31⋊C3), C2×C5⋊#14559023, C2×C5⋊#14559022, …
maximal normal subgroup ofC2×C13×C5⋊(D31⋊C3), C2×C5⋊#14559023, C2×C5⋊#14559022, …
maximal quotient ofD3×C13×D155, C2×C3×C13×D155, C2×C13×D465

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8060, 42);