Finite Group Databasebeta

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C32×Dic191⋊C5 #46805985

order34380
automorphism?
homologyAbelianization (H1) = C32×C4×C5 · Schur multiplier (H2) = C3

Aliases

direct productC32×Dic191⋊C5
unambiguous semidirect productDic191⋊(C32×C5)
unambiguous semidirect product(C191⋊C5)⋊(C32×C4)
unambiguous semidirect product(C3×Dic191)⋊(C3×C5)
unambiguous semidirect product(C32×Dic191)⋊C5

Splittings

derived, SylowC191 ⋊ C32×C4×C5
HallC32×C191⋊C5 ⋊ C4
HallC32×Dic191 ⋊ C5
HallC32×C191 ⋊ C4×C5
HallC191⋊C5 ⋊ C32×C4
HallDic191 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC2×C32D191⋊C5
commutator, hypocenterC191C32×C4×C5
FrattiniC2C32×D191⋊C5
Fitting, socleC2×C32×C191C2×C5
prime radicalC2×C32×C191⋊C5C2
cosocleC2×C191C2×C32×C5
LCSG ▷ C191
UCSC1 ◁ C2×C32

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6876

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34380, 40);