Finite Group Databasebeta

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C32×C5×C17×Dic7 #36339335

order21420
automorphism?
homologyAbelianization (H1) = C32×C4×C5×C17 · Schur multiplier (H2) = C3

Aliases

direct productC32×C5×C17×Dic7

Splittings

derived, SylowC7 ⋊ C32×C4×C5×C17
HallC32×C5×C7×C17 ⋊ C4
HallC32×C7×C17 ⋊ C4×C5
HallC5×C7×C17 ⋊ C32×C4
HallC32×C5×C7 ⋊ C4×C17
HallC7×C17 ⋊ C32×C4×C5
HallC32×C7 ⋊ C4×C5×C17
HallC5×C7 ⋊ C32×C4×C17

Subgroups

subgroupG/H
center, hypercenterC2×C32×C5×C17D7
commutator, hypocenterC7C32×C4×C5×C17
FrattiniC2C32×C5×D7×C17
Fitting, socle, prime radicalC2×C32×C5×C7×C17C2
cosocleC2×C7C2×C32×C5×C17
LCSG ▷ C7
UCSC1 ◁ C2×C32×C5×C17

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 21420

Conjugacy classes & character table

7650 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21420, 167);