Finite Group Databasebeta

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C22×C52⋊#63270 #41032086

order27300
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C5

Aliases

direct productC22×C52⋊#63270

Splittings

Fitting, socle, HallC22×C52×C7×C13 ⋊ C3
derived, HallC52×C7×C13 ⋊ C22×C3
HallC22×C52×C13 ⋊ ΓL(1,𝔽8)
HallC22×C52×C7 ⋊ C13⋊C3
HallC22×C7×C13 ⋊ C52⋊C3
HallC52×C13 ⋊ C22×ΓL(1,𝔽8)
HallC52×C7 ⋊ C22×C13⋊C3
HallC22×C52 ⋊ #63270
HallC7×C13 ⋊ C22×C52⋊C3
HallC22×C13 ⋊ C7⋊(C52⋊C3)
HallC22×C7 ⋊ C13⋊(C52⋊C3)
SylowC52 ⋊ C22×#63270
SylowC13 ⋊ C22×C7⋊(C52⋊C3)
SylowC7 ⋊ C22×C13⋊(C52⋊C3)

Subgroups

subgroupG/H
center, hypercenterC22C52⋊#63270
commutator, cosocle, hypocenterC52×C7×C13C22×C3
FrattiniC1G
Fitting, socleC22×C52×C7×C13C3
LCSG ▷ C52×C7×C13
UCSC1 ◁ C22

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5460

Conjugacy classes & character table

3044 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27300, 976);