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C7×Dic1235 #46829121

order34580
automorphism?
homologyAbelianization (H1) = C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×Dic1235
unambiguous semidirect productC19⋊(C7×Dic65)

Splittings

derived, HallC5×C13×C19 ⋊ C4×C7
HallC5×C7×C13×C19 ⋊ C4
HallC7×C13×C19 ⋊ Dic5
HallC5×C7×C19 ⋊ Dic13
HallC5×C7×C13 ⋊ Dic19
HallC13×C19 ⋊ C7×Dic5
HallC7×C19 ⋊ Dic65
HallC5×C19 ⋊ C7×Dic13
HallC7×C13 ⋊ Dic95
HallC5×C13 ⋊ C7×Dic19
HallC5×C7 ⋊ Dic247
SylowC19 ⋊ C7×Dic65
SylowC13 ⋊ C7×Dic95
SylowC5 ⋊ C7×Dic247

Subgroups

subgroupG/H
center, hypercenterC2×C7D1235
commutator, hypocenterC5×C13×C19C4×C7
FrattiniC2C7×D1235
Fitting, socle, prime radicalC2×C5×C7×C13×C19C2
cosocleC2×C5×C13×C19C2×C7
LCSG ▷ C5×C13×C19
UCSC1 ◁ C2×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 34580

Conjugacy classes & character table

8666 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34580, 12);