Finite Group Databasebeta

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C7×D1785 #38736000

order24990
automorphism?
homologyAbelianization (H1) = C2×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×D1785
unambiguous semidirect productC3⋊(C7×D595)
unambiguous semidirect productC5⋊(C7×D357)
unambiguous semidirect productC7⋊(C7×D255)
unambiguous semidirect productC17⋊(C7×D105)

Splittings

Fitting, socle, HallC3×C5×C72×C17 ⋊ C2
derivedC3×C5×C7×C17 ⋊ C2×C7
HallC5×C72×C17 ⋊ D3
HallC3×C72×C17 ⋊ D5
HallC72×C17 ⋊ D15
HallC3×C5×C72 ⋊ D17
HallC3×C5×C17 ⋊ C7×D7
HallC5×C72 ⋊ D51
HallC3×C72 ⋊ D85
HallC5×C17 ⋊ C7×D21
HallC3×C17 ⋊ C7×D35
SylowC72 ⋊ D255
SylowC17 ⋊ C7×D105
HallC3×C5 ⋊ C7×D119
SylowC5 ⋊ C7×D357
SylowC3 ⋊ C7×D595

Subgroups

subgroupG/H
center, hypercenterC7D1785
commutator, cosocle, hypocenterC3×C5×C7×C17C2×C7
FrattiniC1G
Fitting, socleC3×C5×C72×C17C2
LCSG ▷ C3×C5×C7×C17
UCSC1 ◁ C7

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3570

Conjugacy classes & character table

6258 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24990, 90);