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C2×D7×C13⋊(C52⋊C3) #41031832

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

Aliases

direct productC2×D7×C13⋊(C52⋊C3)

Splittings

Fitting, socleC2×C52×C7×C13 ⋊ C2×C3
derived, HallC52×C7×C13 ⋊ C22×C3
HallC2×C52×C13×D7 ⋊ C3
HallC7×C13⋊(C52⋊C3) ⋊ C22
HallC2×C52×D7 ⋊ C13⋊C3
HallC2×C13×D7 ⋊ C52⋊C3
HallC52×C13 ⋊ C2×C3×D7
HallC52×C7 ⋊ C22×C13⋊C3
HallC7×C13 ⋊ C22×C52⋊C3
SylowC52 ⋊ C2×D7×C13⋊C3
SylowC13 ⋊ C2×D7×C52⋊C3
SylowC7 ⋊ C22×C13⋊(C52⋊C3)

Subgroups

subgroupG/H
center, hypercenterC2D7×C13⋊(C52⋊C3)
commutator, cosocle, hypocenterC52×C7×C13C22×C3
FrattiniC1G
Fitting, socleC2×C52×C7×C13C2×C3
LCSG ▷ C52×C7×C13
UCSC1 ◁ C2

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2730

Conjugacy classes & character table

1110 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27300, 722);