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Dic3×C25×C71 #36319014

order21300
automorphism?
homologyAbelianization (H1) = C4×C25×C71 · Schur multiplier (H2) = C1

Aliases

direct productDic3×C25×C71
unambiguous semidirect productC3⋊(C4×C25×C71)

Splittings

derived, SylowC3 ⋊ C4×C25×C71
HallC3×C25×C71 ⋊ C4
HallC3×C71 ⋊ C4×C25
HallC3×C25 ⋊ C4×C71

Subgroups

subgroupG/H
center, hypercenterC2×C25×C71D3
commutator, hypocenterC3C4×C25×C71
FrattiniC2×C5C5×D3×C71
FittingC2×C3×C25×C71C2
socle, prime radicalC2×C3×C5×C71C2×C5
cosocleC2×C3×C5C2×C5×C71
LCSG ▷ C3
UCSC1 ◁ C2×C25×C71

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 21300

Conjugacy classes & character table

10650 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21300, 6);