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C3×C13×Dic161 #38737291

order25116
automorphism?
homologyAbelianization (H1) = C3×C4×C13 · Schur multiplier (H2) = C1

Aliases

direct productC3×C13×Dic161
unambiguous semidirect productC23⋊(C3×C13×Dic7)

Splittings

derived, HallC7×C23 ⋊ C3×C4×C13
HallC3×C7×C13×C23 ⋊ C4
HallC7×C13×C23 ⋊ C3×C4
HallC3×C13×C23 ⋊ Dic7
HallC3×C7×C23 ⋊ C4×C13
HallC13×C23 ⋊ C3×Dic7
HallC3×C7×C13 ⋊ Dic23
HallC7×C13 ⋊ C3×Dic23
HallC3×C23 ⋊ C13×Dic7
SylowC23 ⋊ C3×C13×Dic7
HallC3×C7 ⋊ C13×Dic23
SylowC7 ⋊ C3×C13×Dic23

Subgroups

subgroupG/H
center, hypercenterC2×C3×C13D161
commutator, hypocenterC7×C23C3×C4×C13
FrattiniC2C3×C13×D161
Fitting, socle, prime radicalC2×C3×C7×C13×C23C2
cosocleC2×C7×C23C2×C3×C13
LCSG ▷ C7×C23
UCSC1 ◁ C2×C3×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 25116

Conjugacy classes & character table

6396 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25116, 10);