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C32×C5×#10621725 #44477865

order30420
automorphism?
homologyAbelianization (H1) = C32×C4×C5 · Schur multiplier (H2) = C3×C13

Aliases

direct productC32×C5×#10621725

Splittings

derived, SylowC132 ⋊ C32×C4×C5
HallC32×C5×C132 ⋊ C4
HallC32×C132 ⋊ C4×C5
HallC5×C132 ⋊ C32×C4

Subgroups

subgroupG/H
center, hypercenterC2×C32×C5C13⋊D13
commutator, hypocenterC132C32×C4×C5
FrattiniC2C32×C5×C13⋊D13
Fitting, socle, prime radicalC2×C32×C5×C132C2
cosocleC2×C132C2×C32×C5
LCSG ▷ C132
UCSC1 ◁ C2×C32×C5

576 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 30420

Conjugacy classes & character table

7740 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30420, 454);