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C7×Dic103⋊C9 #39906641

order25956
automorphism?
homologyAbelianization (H1) = C4×C7×C9 · Schur multiplier (H2) = C1

Aliases

direct productC7×Dic103⋊C9
unambiguous semidirect productDic103⋊(C7×C9)
unambiguous semidirect product(C103⋊C9)⋊(C4×C7)

Splittings

derived, SylowC103 ⋊ C4×C7×C9
HallC7×C103⋊C9 ⋊ C4
HallC7×Dic103 ⋊ C9
HallC103⋊C9 ⋊ C4×C7
HallC7×C103 ⋊ C4×C9
HallDic103 ⋊ C7×C9

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7D103⋊C3
commutator, hypocenterC103C4×C7×C9
FrattiniC2×C3C7×D103⋊C3
Fitting, socle, prime radicalC2×C3×C7×C103C2×C3
cosocleC2×C3×C103C2×C3×C7
LCSG ▷ C103
UCSC1 ◁ C2×C3×C7

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 25956

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25956, 13);