Finite Group Databasebeta

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C3×Dic7×C11⋊C25 #37528210

order23100
automorphism?
homologyAbelianization (H1) = C3×C4×C25 · Schur multiplier (H2) = C1

Aliases

direct productC3×Dic7×C11⋊C25
unambiguous semidirect product(C3×C11×Dic7)⋊C25

Splittings

derived, HallC7×C11 ⋊ C3×C4×C25
HallC3×C7×C11⋊C25 ⋊ C4
HallC7×C11⋊C25 ⋊ C3×C4
HallC3×C11×Dic7 ⋊ C25
HallC11×Dic7 ⋊ C3×C25
HallC3×C7×C11 ⋊ C4×C25
HallC3×C11 ⋊ C25×Dic7
HallC3×C7 ⋊ C4×C11⋊C25
SylowC11 ⋊ C3×C25×Dic7
SylowC7 ⋊ C3×C4×C11⋊C25

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5D7×C11⋊C5
commutator, hypocenterC7×C11C3×C4×C25
FrattiniC2×C5C3×D7×C11⋊C5
Fitting, socle, prime radicalC2×C3×C5×C7×C11C2×C5
cosocleC2×C5×C7×C11C2×C3×C5
LCSG ▷ C7×C11
UCSC1 ◁ C2×C3×C5

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 23100

Conjugacy classes & character table

1050 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 21);