Finite Group Databasebeta

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C2×C52⋊#63270 #28331645

order13650
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C5

Aliases

direct productC2×C52⋊#63270
unambiguous semidirect product(C2×C52)⋊#63270

Splittings

Fitting, socle, HallC2×C52×C7×C13 ⋊ C3
derived, HallC52×C7×C13 ⋊ C2×C3
HallC2×C52×C13 ⋊ ΓL(1,𝔽8)
HallC2×C52×C7 ⋊ C13⋊C3
HallC52×C13 ⋊ C2×ΓL(1,𝔽8)
HallC2×C7×C13 ⋊ C52⋊C3
HallC52×C7 ⋊ C2×C13⋊C3
HallC7×C13 ⋊ C2×C52⋊C3
HallC2×C52 ⋊ #63270
HallC2×C13 ⋊ C7⋊(C52⋊C3)
SylowC52 ⋊ C2×#63270
HallC2×C7 ⋊ C13⋊(C52⋊C3)
SylowC13 ⋊ C2×C7⋊(C52⋊C3)
SylowC7 ⋊ C2×C13⋊(C52⋊C3)

Subgroups

subgroupG/H
center, hypercenterC2C52⋊#63270
commutator, cosocle, hypocenterC52×C7×C13C2×C3
FrattiniC1G
Fitting, socleC2×C52×C7×C13C3
LCSG ▷ C52×C7×C13
UCSC1 ◁ C2

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2730

Conjugacy classes & character table

1522 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#41031401, #41031403, #41031407, …
maximal normal subgroup of#41031401, #41031403, #41031407, …
maximal quotient ofC4×C52⋊#63270, C22×C52⋊#63270

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13650, 133);