Finite Group Databasebeta

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C5×C7⋊C9×C107 #46797808

order33705
automorphism?
homologyAbelianization (H1) = C5×C9×C107 · Schur multiplier (H2) = C1

Aliases

direct productC5×C7⋊C9×C107
unambiguous semidirect productC7⋊(C5×C9×C107)
unambiguous semidirect product(C5×C7)⋊(C9×C107)
unambiguous semidirect product(C7×C107)⋊(C5×C9)
unambiguous semidirect product(C5×C7×C107)⋊C9

Splittings

derived, SylowC7 ⋊ C5×C9×C107
HallC5×C7×C107 ⋊ C9
HallC7×C107 ⋊ C5×C9
HallC5×C7 ⋊ C9×C107

Subgroups

subgroupG/H
center, hypercenterC3×C5×C107ΓL(1,𝔽8)
commutator, hypocenterC7C5×C9×C107
FrattiniC3C5×ΓL(1,𝔽8)×C107
Fitting, socle, prime radicalC3×C5×C7×C107C3
cosocleC3×C7C3×C5×C107
LCSG ▷ C7
UCSC1 ◁ C3×C5×C107

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 33705

Conjugacy classes & character table

8025 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33705, 2);