Finite Group Databasebeta

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C3×Dic3×C23×C37 #44499658

order30636
automorphism?
homologyAbelianization (H1) = C3×C4×C23×C37 · Schur multiplier (H2) = C1

Aliases

direct productC3×Dic3×C23×C37
unambiguous semidirect productC3⋊(C3×C4×C23×C37)

Splittings

derivedC3 ⋊ C3×C4×C23×C37
HallC32×C23×C37 ⋊ C4
HallC32×C37 ⋊ C4×C23
HallC32×C23 ⋊ C4×C37
SylowC32 ⋊ C4×C23×C37

Subgroups

subgroupG/H
center, hypercenterC2×C3×C23×C37D3
commutator, hypocenterC3C3×C4×C23×C37
FrattiniC2C3×D3×C23×C37
Fitting, socle, prime radicalC2×C32×C23×C37C2
cosocleC2×C3C2×C3×C23×C37
LCSG ▷ C3
UCSC1 ◁ C2×C3×C23×C37

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10212

Conjugacy classes & character table

15318 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30636, 61);