Finite Group Databasebeta

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C5×C7×#11760330 #49141517

order36540
automorphism?
homologyAbelianization (H1) = C4×C5×C7 · Schur multiplier (H2) = C3

Aliases

direct productC5×C7×#11760330

Splittings

Fitting, socle, HallC32×C5×C7×C29 ⋊ C4
derived, HallC32×C29 ⋊ C4×C5×C7
HallC32×C7×C29 ⋊ C4×C5
HallC32×C5×C29 ⋊ C4×C7
HallC5×C7×C29 ⋊ #157
HallC32×C5×C7 ⋊ Dic29
HallC7×C29 ⋊ C5×#157
HallC5×C29 ⋊ C7×#157
HallC32×C7 ⋊ C5×Dic29
HallC32×C5 ⋊ C7×Dic29
SylowC29 ⋊ C5×C7×#157
SylowC32 ⋊ C5×C7×Dic29

Subgroups

subgroupG/H
center, hypercenterC5×C7#11760330
commutator, hypocenterC32×C29C4×C5×C7
FrattiniC1G
Fitting, socleC32×C5×C7×C29C4
prime radicalC5×C7×C3⋊D3×C29C2
cosocleC3⋊D3×C29C2×C5×C7
LCSG ▷ C32×C29
UCSC1 ◁ C5×C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6090

Conjugacy classes & character table

3150 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36540, 359);