Finite Group Databasebeta

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C5×#10621725⋊C7 #37556808

order23660
automorphism?
homologyAbelianization (H1) = C4×C5×C7 · Schur multiplier (H2) = C13

Aliases

direct productC5×#10621725⋊C7
unambiguous semidirect product#10621725⋊(C5×C7)
unambiguous semidirect product(C5×#10621725)⋊C7

Splittings

derived, SylowC132 ⋊ C4×C5×C7
HallC5×C132⋊C7 ⋊ C4
HallC5×#10621725 ⋊ C7
HallC132⋊C7 ⋊ C4×C5
HallC5×C132 ⋊ C4×C7
Hall#10621725 ⋊ C5×C7

Subgroups

subgroupG/H
center, hypercenterC2×C5(C13⋊D13)⋊C7
commutator, hypocenterC132C4×C5×C7
FrattiniC2C5×(C13⋊D13)⋊C7
Fitting, socleC2×C5×C132C2×C7
prime radicalC2×C5×C132⋊C7C2
cosocleC2×C132C2×C5×C7
LCSG ▷ C132
UCSC1 ◁ C2×C5

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1820

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23660, 38);