Finite Group Databasebeta

← Prev (#41032090) Next (#41032092) →

C22×C52×#63271 #41032091

order27300
automorphism?
homologyAbelianization (H1) = C22×C3×C52 · Schur multiplier (H2) = C2×C5

Aliases

direct productC22×C52×#63271

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC22×C52#63271
commutator, cosocle, hypocenterC7×C13C22×C3×C52
FrattiniC1G
Fitting, socleC22×C52×C7×C13C3
LCSG ▷ C7×C13
UCSC1 ◁ C22×C52

320 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9100

Conjugacy classes & character table

3300 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27300, 981);