Finite Group Databasebeta

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C7×Dic825 #37528206

order23100
automorphism?
homologyAbelianization (H1) = C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×Dic825
unambiguous semidirect productC3⋊(C7×Dic275)
unambiguous semidirect productC11⋊(C7×Dic75)

Splittings

derived, HallC3×C11×C25 ⋊ C4×C7
HallC3×C7×C11×C25 ⋊ C4
HallC7×C11×C25 ⋊ Dic3
HallC3×C7×C25 ⋊ Dic11
HallC11×C25 ⋊ C7×Dic3
HallC3×C7×C11 ⋊ Dic25
HallC7×C25 ⋊ Dic33
HallC7×C11 ⋊ Dic75
HallC3×C25 ⋊ C7×Dic11
HallC3×C11 ⋊ C7×Dic25
SylowC25 ⋊ C7×Dic33
HallC3×C7 ⋊ Dic275
SylowC11 ⋊ C7×Dic75
SylowC3 ⋊ C7×Dic275

Subgroups

subgroupG/H
center, hypercenterC2×C7D825
commutator, hypocenterC3×C11×C25C4×C7
FrattiniC2×C5C7×D165
FittingC2×C3×C7×C11×C25C2
socle, prime radicalC2×C3×C5×C7×C11D5
cosocleC2×C3×C11×C25C2×C7
LCSG ▷ C3×C11×C25
UCSC1 ◁ C2×C7

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 23100

Conjugacy classes & character table

5796 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 17);