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C2×C5×#15693074 #45682121

order32970
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC2×C5×#15693074

Splittings

Fitting, socle, HallC2×C5×C7×C157 ⋊ C3
derived, HallC7×C157 ⋊ C2×C3×C5
HallC5×C7×C157 ⋊ C2×C3
HallC2×C7×C157 ⋊ C3×C5
HallC2×C5×C157 ⋊ ΓL(1,𝔽8)
HallC5×C157 ⋊ C2×ΓL(1,𝔽8)
HallC2×C157 ⋊ C5×ΓL(1,𝔽8)
SylowC157 ⋊ C2×C5×ΓL(1,𝔽8)
HallC2×C5×C7 ⋊ C157⋊C3
HallC5×C7 ⋊ C2×C157⋊C3
HallC2×C7 ⋊ C5×C157⋊C3
SylowC7 ⋊ C2×C5×C157⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C5#15693074
commutator, cosocle, hypocenterC7×C157C2×C3×C5
FrattiniC1G
Fitting, socleC2×C5×C7×C157C3
LCSG ▷ C7×C157
UCSC1 ◁ C2×C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10990

Conjugacy classes & character table

3690 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32970, 5);