Finite Group Databasebeta

#44476173

order30304
automorphism?
homologyAbelianization (H1) = C2×C4 · Schur multiplier (H2) = C2

Aliases

No aliases for this group.

Splittings

SylowC947 ⋊ #103

Subgroups

subgroupG/H
centerC22C22⋊D947
commutatorC4×C947C2×C4
FrattiniC2×C4C2×D947
FittingC4⋊C4×C947C2
socle, prime radicalC22×C947D4
cosocleC2×C4×C947C22
hypercenterC4⋊C4D947
hypocenterC947#103
LCSG ▷ C4×C947 ▷ C2×C947 ▷ C947
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

42 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 30304

Polycyclic presentation:

2^5,947|a^2=d,b^2=e,c^2=e,b^a=bc,c^a=ce,c^b=ce,f^b=f^946

Conjugacy classes & character table

4744 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30304, 69);