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C2×#28331638 #41031827

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

Aliases

direct productC2×#28331638

Splittings

Fitting, socleC2×C52×C7×C13 ⋊ C2×C3
derived, HallC52×C7×C13 ⋊ C22×C3
HallC2×C52×C7×D13 ⋊ C3
HallC52⋊#63270 ⋊ C22
HallC2×C52×D13 ⋊ ΓL(1,𝔽8)
HallC2×C7×D13 ⋊ C52⋊C3
HallC52×C13 ⋊ C22×ΓL(1,𝔽8)
HallC52×C7 ⋊ C2×D13⋊C3
HallC7×C13 ⋊ C22×C52⋊C3
HallC2×D13 ⋊ C7⋊(C52⋊C3)
SylowC52 ⋊ C2×#10587716
SylowC13 ⋊ C22×C7⋊(C52⋊C3)
SylowC7 ⋊ C2×D13⋊(C52⋊C3)

Subgroups

subgroupG/H
center, hypercenterC2#28331638
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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27300, 717);