Finite Group Databasebeta

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C5×C7⋊#11760330 #49141520

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

Aliases

direct productC5×C7⋊#11760330
unambiguous semidirect productC7⋊(C5×#11760330)

Splittings

Fitting, socle, HallC32×C5×C7×C29 ⋊ C4
derived, HallC32×C7×C29 ⋊ C4×C5
HallC32×C5×C29 ⋊ Dic7
HallC5×C7×C29 ⋊ #157
HallC32×C5×C7 ⋊ Dic29
HallC32×C29 ⋊ C5×Dic7
HallC7×C29 ⋊ C5×#157
HallC5×C29 ⋊ C7⋊#157
HallC32×C7 ⋊ C5×Dic29
HallC32×C5 ⋊ Dic203
HallC5×C7 ⋊ #11760330
SylowC29 ⋊ C5×C7⋊#157
SylowC32 ⋊ C5×Dic203
SylowC7 ⋊ C5×#11760330

Subgroups

subgroupG/H
center, hypercenterC5C7⋊#11760330
commutator, hypocenterC32×C7×C29C4×C5
FrattiniC1G
Fitting, socleC32×C5×C7×C29C4
prime radicalC5×C7×C3⋊D3×C29C2
cosocleC7×C3⋊D3×C29C2×C5
LCSG ▷ C32×C7×C29
UCSC1 ◁ C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6090

Conjugacy classes & character table

3060 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36540, 362);