Finite Group Databasebeta

#44473379

order30032
automorphism?
homologyAbelianization (H1) = C2×C4 · Schur multiplier (H2) = C2

Aliases

No aliases for this group.

Splittings

SylowC1877 ⋊ C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC22C2×D1877
commutatorC2×C1877C2×C4
FittingC2×C4×C1877C2
socle, prime radical, cosocleC22×C1877C22
hypercenterC2×C4D1877
hypocenterC1877C4⋊C4
LCSG ▷ C2×C1877 ▷ C1877
UCSC1 ◁ C22 ◁ C2×C4

26 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 30032

Polycyclic presentation:

2^4,1877|a^2=d,b^2=c,b^a=bc,e^b=e^1876

Conjugacy classes & character table

7514 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30032, 19);