Finite Group Databasebeta

← Prev (#37528201) Next (#37528203) →

C7×C25×Dic33 #37528202

order23100
automorphism?
homologyAbelianization (H1) = C4×C7×C25 · Schur multiplier (H2) = C1

Aliases

direct productC7×C25×Dic33
unambiguous semidirect productC3⋊(C7×C25×Dic11)

Splittings

derived, HallC3×C11 ⋊ C4×C7×C25
HallC3×C7×C11×C25 ⋊ C4
HallC7×C11×C25 ⋊ Dic3
HallC3×C11×C25 ⋊ C4×C7
HallC3×C7×C25 ⋊ Dic11
HallC11×C25 ⋊ C7×Dic3
HallC3×C7×C11 ⋊ C4×C25
HallC7×C11 ⋊ Dic3×C25
HallC3×C25 ⋊ C7×Dic11
HallC3×C7 ⋊ C25×Dic11
SylowC11 ⋊ C7×Dic3×C25
SylowC3 ⋊ C7×C25×Dic11

Subgroups

subgroupG/H
center, hypercenterC2×C7×C25D33
commutator, hypocenterC3×C11C4×C7×C25
FrattiniC2×C5C5×C7×D33
FittingC2×C3×C7×C11×C25C2
socle, prime radicalC2×C3×C5×C7×C11C2×C5
cosocleC2×C3×C5×C11C2×C5×C7
LCSG ▷ C3×C11
UCSC1 ◁ C2×C7×C25

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 23100

Conjugacy classes & character table

6300 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 13);